If you are using the mean for the average (which is quite common), then it is completely possible for most people to have their IQ be above average (not saying it is, just saying there's nothing mathematically wrong if it is).

Except that IQs are explicitly made to fit a normal distribution.

Well, half of them are correct (assuming a normal distribution, which IQ tests have by design).

The "middle" class has never been defined as any kind of "average" class.